Generalized Least Squares

Generalised Least Squares adopts a concise and mathematically rigorous approach. It will provide an up-to-date self-contained introduction to the unified theory of generalized least squares estimations, adopting a concise and mathematically rigorous approach. The book covers in depth the 'lower and upper bounds approach', pioneered by the first author, which is widely regarded as a very powerful and useful tool for generalized least squares estimation, helping the reader develop their understanding of the theory. The book also contains exercises at the end of each chapter and applications to statistics, econometrics, and biometrics, enabling use for self-study or as a course text.

Generalised Least Squares adopts a concise andmathematically rigorous approach. It will provide anup-to-date self-contained introduction to the unified theory ofgeneralized least squares estimations, adopting a concise andmathematically rigorous approach. The book covers in depth the'lower and upper bounds approach', pioneered by the first authorwhich is widely regarded as a very powerful and useful tool forgeneralized least squares estimation, helping the reader developtheir understanding of the theory. The book also contains exercisesat the end of each chapter and applications to statisticseconometrics, and biometrics, enabling use for self-study or as acourse text.

Preface.1 Preliminaries.1.1 Overview.1.2 Multivariate Normal and Wishart Distributions.1.3 Elliptically Symmetric Distributions.1.4 Group Invariance.1.5 Problems.2 Generalized Least Squares Estimators.2.1 Overview.2.2 General Linear Regression Model.2.3 Generalized Least Squares Estimators.2.4 Finiteness of Moments and Typical GLSEs.2.5 Empirical Example: CO2 Emission Data.2.6 Empirical Example: Bond Price Data.2.7 Problems.3 Nonlinear Versions of the Gauss-MarkovTheorem.3.1 Overview.3.2 Generalized Least Squares Predictors.3.3 A Nonlinear Version of the Gauss-Markov Theorem inPrediction.3.4 A Nonlinear Version of the Gauss-Markov Theorem inEstimation.3.5 An Application to GLSEs with Iterated Residuals.3.6 Problems.4 SUR and Heteroscedastic Models.4.1 Overview.4.2 GLSEs with a Simple Covariance Structure.4.3 Upper Bound for the Covariance Matrix of a GLSE.4.4 Upper Bound Problem for the UZE in an SUR Model.4.5 Upper Bound Problems for a GLSE in a HeteroscedasticModel.4.6 Empirical Example: CO2 Emission Data.4.7 Problems.5 Serial Correlation Model.5.1 Overview.5.2 Upper Bound for the Risk Matrix of a GLSE.5.3 Upper Bound Problem for a GLSE in the Anderson Model.5.4 Upper Bound Problem for a GLSE in a Two-equationHeteroscedastic Model.5.5 Empirical Example: Automobile Data.5.6 Problems.6 Normal Approximation.6.1 Overview.6.2 Uniform Bounds for Normal Approximations to the ProbabilityDensity Functions.6.3 Uniform Bounds for Normal Approximations to the CumulativeDistribution Functions.6.4 Problems.7 Extension of Gauss-Markov Theorem.7.1 Overview.7.2 An Equivalence Relation on S(n).7.3 A Maximal Extension of the Gauss-Markov Theorem.7.4 Nonlinear Versions of the Gauss-Markov Theorem.7.5 Problems.8 Some Further Extensions.8.1 Overview.8.2 Concentration Inequalities for the Gauss-MarkovEstimator.8.3 Efficiency of GLSEs under Elliptical Symmetry.8.4 Degeneracy of the Distributions of GLSEs.8.5 Problems.9 Growth Curve Model and GLSEs.9.1 Overview.9.2 Condition for the Identical Equality between the GME and theOLSE.9.3 GLSEs and Nonlinear Version of the Gauss-MarkovTheorem .9.4 Analysis Based on a Canonical Form.9.5 Efficiency of GLSEs.9.6 Problems.A. Appendix.A.1 Asymptotic Equivalence of the Estimators of theta inthe AR(1) Error Model and Anderson Model.Bibliography.Index.